Problem: The length, width, and height of a rectangular prism are in the ratio $3:2:1$. The length is $9$ in. In cubic inches, what is the volume of the prism?
$3:2:1 = 9:6:3$, so the length, width, and height are $9$, $6$, and $3$ inches, respectively. So, the volume is $9\cdot 6\cdot 3 = \boxed{162}$ cubic inches.